Variable leverage gearing



Feb 17, 1948. ,5 AK 12,436,276

VARIABLE .LEVERAGE GEARING Original Filed Dec. 31, 1940 4 Sheets-Sheet 1 Snocntor ERNES T W-ILDHHBER Feb. 17,- 1948. E. WILDHABER 2,436,276

VARIABLE LEVERAGE GEARING Original Filed Dec. 31, 1940 4 Sheets-Sheet 2 ERNEST W/LDHHB'ER I I 3nnentor' Feb. 17; 1948. WILDHABER I 2,436,275

VARIABLE LEVERAGE GEARING Original Filed Dec. 31, 1940 4'Sheets-Sheet 3 3nventor ER/VES T W/LDHHBEE ,1 I EWILDHABER 2,

VARIABLE LEVERAGE GEARING Original Filed Dec. 31, 1940 4 Sheets-Sheet 4 L Zhwentor ee am e "nr ii ipeum ever ear-we Patented Feb. 17, 1948 e 2,436,276

Ernest- Wildhaber,-=-Brighton{ N; assignon to Gleason 'Works,'Rochester, N. Y., a corporation of New York Wen ati nfie 3 191. ;,.-serie N 372,473- ;eniy i de t s anplic ionlehe r'ua 13, 1 943 Segial No. 475,725. In Great Britain Decembe 31, 1941 "H: *A I .11: Hz a .I-\ l 1 5 i e $325 invention; lgelates to.;gea1's ,Ior fore-generating theetwo ,sidesof the teeth. W,hen transmitting non-unijogm moti onand;to;methonew idehof the gear-teethewas-cut at-a ,time, 1t ods ozfi pr oqucing such geaps and particularly to took longexptowproduce the; gears thann estandard va i ip -levielj egeal san 9 methods Qf- IJI'O; uniiormanotionldifferential gears andetheeosto; ducine th This epp ca ni di /isionof 5 producingthese,varyingelevena e ears w s. n: n1y ,I{ateI1 t 1 Io. zggjgziq which c oyers specifically creased accordinglyeoyerfeunifonm-motion ears. the novel method ogggyjnwntiop. =,The.present whereetwo sides, were generated at. art me, in: application is directeg. to the ,new forn1 of gea.rs. creased complications. were introduced into the t jy g-leverage gears are socal led,because generating.machinegandtthe cost-cf these ma:- the"mating tooth sugiacestof the gears are-LS0 l0 chineslwasincreased:ccrrep ndin f dim;- pl dt a fi be earirctgte together ape' culty has been that while there exists a basgc niodic'vvariationcbetween the gears ein leverage or rack vor crownmgear to -which..- nifq mrmqti toriiii' f-r'eti' -wx 1 such gears paye -been sum or bevellgear gmax be ge em ci ic n a fida .s' egya ,g ula xjimme diffierenr there has. her ofo e ex ede o." lfm nndine i iarl s' d'ff tyuclgsi-ang tractors, wne ip' 15 basic rack' ortcmwn 3. 1; ont-v r in r ev r e i' ifia i WW z fi t t m e h m o l p eve ing ears, and acco din y. it; ha h n im 0 si 1 t9 co'r'riple'te loss' of}tfactiorpwhen one oi, the drive generate such gearq two sigles simultaneously wh' l fi Y .t 1% in w ich eu h with me-sameeenemtm m ticngearserenseu, if he 1};

, p0 e gff ne wh e Afuxthendisadvanta c t prev ou form of isdiiliihi'sihd d S a r p ert ane en;=- he t e ;.heye unit-ted to therctlie'r'whe'e ill be pefigd igally in creased. Thifs'Lperidgiicihcieas .inlpower i in tfdditeienbl nh x w i n PPQeW -Rflkiif s liohtoflthifiiudo? s'iio'w ixiwhich it may have a" '1 "*1.- g :31: Luis t Bathi iai h .Y' 'i i wnbe :Pm iqeq c rx efilx. meuntes m h ne e 11 749.- ;m. v be with -l m' P ibu efiime hnq 115 19 one eleqnm eqther fi he e t 'a d bevel gears aie xnoist'ly, e? ed in automotive 1 this; will only cause them to wear the more ,d ifi'eren'tials', flamingleverage th babes have rapidly. I l T e 30 ea nee ex xra ve a e gea hav heret fpt e e us nlx ..exi es,w ere icsmeide .@1 0}1= m of production, etc.

varyjngfleveiageeffect s obtained tooth profiles with. dist tlfy difi 'e large and smalliqi ivatu e: respec ay,

In, thejprevious'ly .kn'ow1'1ioim M '4 garage gears, ea ch tooth Dfdlfil ha ha a portion ofv largeer'a'diuskif cuifvatui 'ekten ion-the greater portionoflethejh'e'igh ofth p'O'rtiOn df mUbh'SiIiaHQr a 1 tending for only a, .viei ymsh' R I t height offthe tooth adjacentj the tip f the tooth. When, these. priorktype varym g 1 erag gear; rolletogether; thevsho n nea each tooth has'a. ma 1 n 1"m,of e 'li' wi ht fi llr" i e, T hence'tends to we awyas'olthe gears" radu; ally-losetheir. vaiying' '.-levera"g The piei/io'us1y, known fonn has hat; the additional uisa'dvantg 'teitftakes pfactic 11y",

5- 1; wa tri r iqn a i twicei e e t i qrtl em t curved portion gt .tip ot the tooth as it does to generate the'main portion of the tooth px files. Funthen than this th preuiouslyv kn wn' e' e baq o I g 'membei-such as a w th'i m; es e e ew ethf t e uir w .ee emtepmmeee e th time or to use two difierent generating fictions i iq n t ifea;

varyin'g leverage V A further object of the invention is to provide-a, 3

tooth shape for varying-leverage gears that can game a g be generated conjugate to the teeth of a basic rack or crown gear that is of such form that contact between the basic generating rack or crown gear and the two members of a pair of mating varying-leverage gears occurs along. the same Another Object of the P esent invention is to lines as between the two gears themselves.

P vi v y ng-leverage gears which will mesh with localized tooth bearing, To this end, I propose to employ for the first time teeth-that are curved longitudinally. I have found that the varying-leverage effect will still be retained in spite of the lengthwise curvature of the teeth.

Longitudinally curved teeth have been pro-. posed heretofore at various times for differential gears, but only in connection with. uniformmotion tooth profile shapes and teeth curved lengthwise at very high spiral angles for the purpose of obtaining a semi-locking effect. I propose to make the new varying-leverage differ- "ential gears with teeth of zero or relatively low spiral angle. a

Bevel gears theoretically should be provided with teeth tapering in depth from end to end. Where they are cut with a face-mill gear cutter, however, such asis ordinarily employed in the cutting of longitudinally curved tooth bevel gears, the mating toothsurfaces produced will not matchexactly and the gears willha've a bias bearing when'run in mesh, that is, a

bearing or contact which extends diagonally of the tooth surfaces from the top of the tooth-at one end to the bottom of the tooth at the other end. Such a for'm'of bearing is objectionable because it causes noise and improper distribution of the tooth loads. 1 f A further object of the present invention, therefore, is to provide a form of varying-lever age gearing having longitudinally curved teeth which will mesh without bias bearing V v Still another object of the invention is to provide varying-leverage tooth shapes which may be cut practically with face mill gearcutter's having outside cutting edges of convex spherical form and inside-cutting edges of concave spherical shape.

such gearing in all types of automotive vehicles.

Other objects of the invention will be app t hereinafter from the specification and from the recital of the appended claims.

" In the drawings:

Fig. 1 is a more or less diagrammatic view, showing the shape of a pinion tooth of a' given pressure angle made according to one-embodiment of the present invention, and illustrating, for the purposes of comparison, the profile shapes of an involute tooth and of the prior form of vary ing-leverage tooth, which are of the same pressure angle as the new tooth;

Fig. 2 is a fragmentary plan view of a pair of longitudinally curved tooth bevel gears made according to one embodiment of the present invention;

Fig. 3 is a diagrammatic view, illustrating the tooth shapes of a pair of gears made according to one embodiment of the present invention and showing that both members of the pair may be made conjugate to a basic rack or crown gear having plane tooth sides;

Fig. 4 is a diagrammatic view showing the undulatory forms of the pitch lines of these gears and of the basic gear to which the gears are generated conjugate; a Fig. 5 Ba diagrammatic view, illustrating certain of-the problems encountered in production .of longitudinally curved tooth gears that have teeth of tapering depth from end to end;

Fig. 6 is a diagrammatic view similar to Fig. 3, illustrating a further embodiment of the invention and showing how a pair of gears may be provided with tooth profiles conjugate to a crown gear having spherical tooth surfaces;

Fig. 7 is a diagrammatic view,-showing the gears of Fig. 6 in another meshing position; and

Figs. 8 and 9 are diagrammatic views, illustrating the preferred method of producing gears according to the present invention. As-has already been indicated, in prior forms of varying-leverage gearing, the tooth profiles were composed of two distinctly different curves, one extending for the greater portion of the height of a tooth and being of greater radius of curvature, and the other lying adjacent the top of the tooth and being of the smaller radius of curvature. In gears made according to the present invention, the variation in leverage is again obtained by making each tooth profile a composite of distinctly difierent curves. In the present case, however, the portion of the tooth profile adjacent to the pitch line is made of small radius of curvature and the portions of the profile above and below the pitch line portion are made of larger radius of curvature. This new profile shape will produce the desired variation in leverage and it has the advantage that the portion of the tooth profile which is most curved is located at the pitch line where the least sliding, and therefore the least wear, will take place. Hence the gears will have longer life.

V Thenew tooth shape may be used for either spur or bevel gears. It hasthe advantage that lt may be generated conjugate to a basic rack or crown gear whose tooth profiles have no variation in curvature, being simple lines, either straight or curved. The desired tooth shapes may be produced'by rolling the gear blank relative to the cutting tool or tools at a varying ratio as though the gear, which is being cut, were meshing with the basic generating gear which is represented by the tools.

The basic generating gear used in the generation of the tooth profiles has an undulating pitch surface. A prime advantage of the use of this basic member is that two sides of the teeth of a ge'ar'may be cut simultaneously with a tool having straight-sided cutting edges or curved cutting edges of single curvature.

anoint mmway heie'hgtiipr the 'tooth. wn irthe gears? cut with: a race-min g a I ciitterl it" is" possible i to provide different radii of eurvytmre' onthe mating tooth surfaces of pair oi gears so as" as obtain a localization of tooth bearing or contact between such; surfaces, and thus enable thegeaisfto accommodate therrlselvs'readily to variations in" mountings and rw r ow end r iamet a ifiore detailedfdescription of my inve' I Fi 1 -1 have shown a p inion toothi iiig'foi iiosite sidtodth surfaces-1| and it, e:

si feeti eiy; shaped" cepriiir'ig to this ifi'veritifi; lf'or' the pur of illustration and om ar sen, 17h ve'also's'h w'natthe iiight'hand siaee rtne" figure? thetboth' smelter a" ctrrespondmg. in:

vhlutepinion' andof a pinion constructed accordihg'to orie'p'rev'iously; known time "of vary:

mgneveragegearmg. The inv 'olute pinion" pro fliers enote by tlfedash lines mane the pro; tile or the" previously known that" li ef fiiofilesfarbf'the same pressure angle measured at common'point" wand-aretangent to one another atthis point. n p s transmit unif rm-mandated conjugate to a; straight sided rackor'crown gear. TheprO fiIef l4 offth'fprvi'ouslyf knbwn type or varying-leverage earing; isfniuch' less lcurived than the involute I profile I3 fup" 'to"a 'point" I6 and therefore this portion {er the}: known meta pr'ofile 14' extends" entiili 'outside "o'fthe involute' l3 on both sides of the point of contact' l 5. ntfpoin't e',"hw evrfthe profile l4 becomes abruptlymoreeurved sd'that' 'the top" portion M, of the profile bends t ward the m/mute 13. The te t profile :4 of p the prior" type of varying-leverage gearing is,-

thererore', composed'of 'two distinct and differentf portions, one' less curved and one more curved than a- 'corr'sponding involute tooth profile" of wedii'al pi's's urangleor inclination. A v p,

The top ertain" l4" of the prior type of vary; ing-leverage tooth will, when run in mesh with mate T varyirignevemge gear, mesh with the cofnpaifatively fiat-'portion ofthe mating gear trams and on its short length will change its inclination-about twice as much as the less curved mam portion of the profile M. In other words, thnornials at the profile ends of the small portion l4 include an angle about twice as large as th'e' one included by thenormalsat theprofiley ends; and H of the main portion of the tooth;

profiler In generatingthe' prior type of varying generated; asthe angle through which the blank ni'ustjbe turnedwhile the main portion of the profile is being-generated. Hence it takes about twice as long to cut the little top portion of' the profile of the prior form of varying-leverage tooth as it does to cut themain tooth profile.

As will be seen from Fig. 1 the profile IZof'a pinion-tooth made according to the presentinventio'n extends entirely inside of the involute profile J3 I 'he portion of the profile between the points IB and l9 is'more curved thanthe involute profile l3, but the portions below the point l3 and above the point"l8, respectively, are less in olute Qlbfilgx The more curved portion of of'the height of the tooth'afid not at the upper M v I or ar mg' gegaring isden'oted a 14; The t ree (I than the corresponding'portions of-ithe;

.T llu fi a ev i 5m a I. .a made according tofthe' present invent on, I have shown inFigl r th line of action" for the tooth profile '12. I 'lfhisfline of course, isl 'the path'ofl points" of ;,comajct v betwe n theiprdfile [25a d the profileof titans gear he n th 'pa'irg arelrolled wiiirftii time mes fd F r ih ifibiel'r bi e 1 i ha a nel f. ti ehaea 3113317, 'fi o l xiii mi e. in 2." nine fieifi Th h 'nq q S. i.',21-3a i Q:.Z' 4 fehe e n) e ts ea in inaei 1 m endpq rsmiid 9 e re e rt en ore ere n? and be ow themint L9 respe t ve y-i Th venimniswt' confi ed t c s to t e; 6; o oth prqfi swhich ha s rai ht li e .0?

v ng ssh n he ooth nm esmw e so l q stru ed i tha the lines o s when l he. cur e a dt fl har c m r sho n tpq ni n and in Fi .4 imar e o ded Pu u to the point where the wholelin of actioniorms ,one

continuous line with a point of inflection at or ne thepoint ih In i r neuco st u fieqa cordi to h pre t inv nt gn; emm hrw th q i Dwi file at the points of contactintersect the line ct en e 2. ,n tt a ne m nt asflin n orm:

mo se rin b t ntsr fi 111% W daw fihe: l n fi-W m h se vpoint are P i s 9 the hi ngr n enia e a s a 9 h ch ter e th cha e iemile. fii q v ra e.

that Q rs h n'f we sea eis ot n o ther.-

te i hep n e shown i Fi l, heek; treme torqueratios areohtained at points and 2| oi the ;line of action;

Opposite side tooth surfaces, i involute gears can, of course, be generated two sides ennui-- taneously, for in;involute gearing; abasic mem' ducedsimultaneouslyby-a generating mOtiOHiiIIL v e arin hen the b a w he e. to turn't hroug-h an angle about twiceas large, while the topportion IV of the pinion; tooth is being;

which the gear,-thatr isto'be produced, isrolledgt relative to the cutting; tool or tools as though it" were meshing with the basic member. V v H There has been no simple basic member,,; however; to which opposite sides of the teeth of' prior types of ;varying,-leverage gears" were conjugate. It has therefore been impossible to gen crate opposite sides :Qf the teeth of such gears" with th ame e a n -motion Sparat gem.

crating motions have had to be used "for produc ing oppositesides to their teeth; Ihave. found,

however, that basic members can be determined for varying-leverage gears constructed according to the present invention. Thus I have found a method of cutting both sides of the teeth of the new varying-leverage gears with the same generating motion; H

In FigQB, I have shown agear 30 and a pinion, ma a c rdi go, one. embodiment. o this in ention inmesh; The 'a gesof the pair "areat j,

32 and 3-3, respectively, and 34 denotes the line of .centers of thepair. Inthisembodimentof the invention, both the gear and the pinion 3| have symmetrical teeth. In the position of mesh shown in Fig. 3, a tooth or the gear 30 is symmetrical with reference to the central plane 34 Containing the axes of the gears. Contact between the mating sides 4|] and 4|, and 42 and 43, respectively, of the teeth of the gear and pinion, is at points 44 and 45 for the position shown,-assuming that there is no backlash between gear and pinion. The normals 46 and 41 to the tooth profiles at points and 45, respectively, then intersect the central plane 34 in point 48 which represents the topmost position of the instantaneous axis of motion between the teeth. The lowest position 49' of the instantaneous axis is attained when one of the pinion teeth is in a position symmetrical to the center line 34, that is, after gear and pinion have rotated together through one half a pitch. It should be noted that the more curved portions 44-50 and 455| of the gear teeth will mesh with the more curved portions 44-52 and:

4553 of the pinion teeth.

I have found that the tooth surfaces 'of both gear 36 and pinion 3|, may be generated conjugate to a basic rack or crown gear 35 having plane tooth sides 36 and 31. 7 Thus a motion can be imparted to a rack or crowngear 35 such that contact between the rack or crown gear and the two gears 30 and 3| occurs along the same lines as between the two gears themselves at any positions of contact. This can be achieved by efiecting a rolling motion at a varying ratio between the tools, which represent the rack or crown gear, and the gear blank during cutting, the-variation in ratio during generation corresponding to variation in ratio between the gears themselves as they rotate in mesh. The motion of the rack or crown gear and the gears 30 and 3|, in other words, is so interrelated that each combination has the same shifting instantaneous axis at all times. We may assume the shift of the instantaneous axis in terms of displacement of the rack or crown gear. As the rack moves through one pitch, the gears 30 and 3i are moved at each instant at a rate determined from the position ofthe instantaneous axis. Corresponding-positions may be computed with the known means in the art.

The basic generating gear 35 used for generating gear 30 and pinion 3| has, then, an undulatory pitch surface 55, as shown in Fig. 4, the extent of whose undulations is determined by the amount of shift of the instantaneous axis of the gears in mesh. The pitch surfaces of the gears 30 and 3! are also undulatory surfaces as denoted at 56 and 51, respectively. The lines 58 and .58 denote the minimum and maximum positions of the instantaneous centers of the gear away from the gear axis, while the lines 59 and 59' denote the minimum and maximum .positions of the instantaneous centers of the pinion away from the pinion axis. The lines 58 and 58 and 59 and 59 denote in other words the minimum and maximum positions of the pitch lines of gear and pinion, respectively.

It will be noted that the undulations of the pitch surfaces of gear and pinion and basic rack correspond to the pitch of the teeth and that the portion of the profile of a gear or pinion tooth which is in action during rotation of the pair of gears through one pitch may be rolled out and generated by motion of the basic rack'or crown gear 35 through one pitch. Much more roll is ters do not match each other suificiently.

required when rollingout the previously known type of varying-leverage gearing with a straight sided rack or crown gear profile, and of course with the previously known form of gearing, it is impossible, as already stated, to generate two sides of the teeth simultaneously from the sam basic rack with a practical tool.

The present invention may be used for spur gears and also for straight bevel gears. In the case of bevel gears, however, it is preferred to make them with longitudinally curved .teeth. Fig. 2 shows such a pair of bevel gears made according to the present invention. In the pair shown, the pinion 60 and the mate gear 6| have longitudinally curved teeth 62 and 63, respectively. These teeth are preferably so curved longitudinally that a line 64 radial of the common apex 65 of the gears will be tangent to the median center line 66 of a tooth at a point midway the length of the tooth. The advantage of longitudinally curved tooth gears is that the mating tooth surfaces of the two members of the pair may be cut with diiferent radii of lengthwise curvature so that they will have less thanfull length contact and have a localization of bearing which is desir-'.- able in bevel gears.

A straight-sided basic member, such as shown at 35 in Fig. 3, may be used as the basic member in generating a pair of spur gears or a Pair. of straight bevel gears according to the present in.- vention, or even in generating longitudinally curved tooth bevel gears provided the teeth are of uniform depth from end to end. It is preferable in bevel gearing, however, to have the teeth taper in depth from end to end.

In the production of longitudinally curved tooth bevel gears, however, there is danger of bias bearing where the gears are cut with facemill cutters of straight tooth profile, that is, with face-mill cutters having conical cutting surfaces.

The mating tooth surfaces will not match and the lines of contact between the mating tooth surfaces will extend diagonally, of the teeth from one end to the other, thus causing the fbias' bearing condition.

The diiiiculty which arises is illustrated inFig. 5. Here 10 denotes a bevel pinion of standard involute form and H is the mate gear. The axes of gear and pinion are located at 12 and 13, respectively. 74 and i5 denote, respectively, the root lines of mating teeth of gear and pinion. In order to cut teeth of tapering depth on the two gears, the face-mill gear cutters employed in cutting their tooth surfaces must have their projected axes at right angles to the root surfaces of the gears. Hence, the cone elements 16 and,

11, respectively, of the cutting surfaces will be perpendicular to the root lines 14 and 15, respec-'{ tively, and will include an angle with each other equal to the taper between the root lines 14 and I5.

spectively, cannot match each other. Accordingly, the tooth surfaces produced by the two out- In the respects noted the problem in the case of gears of varying leverage is the same as the problem for uniform motion gears. In the case of uniform motion gearing, however, there are several different ways of avoiding the bias bearing condition. For instance, the tooth surfaces can be matched to the desired extent, and bias bearing avoided, by modifying the generating motion during the production of the tooth s ur-j, faces. For instance, in the generation of the -39 piniongthia arch-.Bllaofzthecbasic generating-memher, which. is embodied-by .the'ecradlexof: the generating machine, may be so positioned-. that. it does not pass .through the apex -l |rbut will inter- "sect.thepinionaxisJ2inssomeipoint'lli for one sideotthtepiriion teethiand insome point 19 for thetother side-of theipinion teeth. @'In other words, for lone side: of the: "pinion teeth, the axis of the basic;generating gear. may be atiz89 and for the .opposite sideiofxthejteeththeaxis. of th basic: generating gear-izmay (be. at .89".

f The points" and 191' are :spaced' from one another. on opposite sides of. the apex 11. llo cut the" correct tooth profiles; the ratioof roll between gear and cutter is changedsothatinstead: of the instantaneous: axis ofv generation; being .at 82 it will be at 84 for one side of the teeth andrat 85 for .the' oppositesideiof.thezteeth. Through this -procedure,.the toothinorm'alsalong the mean line 82to1the pinion teeth can. beimatchedlto those .of the. gear so 'that 'the'tpinion itooth'surface. has 'the same pressureangle at. any point of mean: line 82 as the gear.toothrsurfacemas atzthe same point. Thexi teeth. insgearf-and pinion will then match alongthewhole length :ofZthe-line 82 and bias bearingis'iavoided. :Thismatchin'g of I the pressure :angles "depends-Ion the "angles; between the lines-82 and 84, "andt821and 85,.and on'the tooth profile itself,,particularlyvits curvature- Now in the case of varying-leverage: gears,:-iwe :have to 'deal" not with oneibut =with' two or'more distince profile curves per tooth side. There isa portion of the :tooth shape which'is'much curved and a'portion which is nearlygflatb Oneiportion requires a larger displacementfpf the cradle 'axis from the cone "apex: of the.v.pinion' and "the other portion requires only a. small displacement. This is true for e'achsideof the teeth. fiThe-m'ethod of eliminating bias bearing, which is usediin standard gears 1 and; which has 1 been described, is. not suitable, therefore, for varying-leveragegears. Nor is any. other ,method;'.; which :has" heretofore been employed foreliminatingcbias in theme.- duction of :uniform motion"z.gears,- suitable :for eliminating bias in the production of gears'of varying-leverage. i I

I havev found, however, thatiifivarying leverage gears are cut .with-afspherioal- 'cuttergtheyimaybe cut with tapering toothzdepth and they will :not have any bias bearing. This is because in 'the case of-a spherical-mutter.'thef direction "of the cutter axis does. notaffect the i'cutting surface. A sphere is ,defined-cOmpIeteIy-by;its radius and its center point, and can be described from axes passing in any and in center point. j. l

In the cutting oi; :longitudinally ."curved. tooth bevel ,1 gears of:varyingdeverage;.ithen, itwis pre-. rferred to;,.use a. sphericalcutterand to: cuttthe gears conjugate toaprowngear having spherical side ;tcothi surfaces,;. 'lihisisillustrated diagram.- matlcaily in Figs. and]. 1. Here strand-9 l denote, respectively, they. ear-and pinion of a pair. of varying-leverage? gears =made-.;according. to one embodiment of this invention. I 1 The axes of these gearsv are 1 at 92=and193,;respectively,:and -94:1is;the line of centers of. the gears. {The tooth surfaces of the -.gears are-generated conjugateto a crown ear. 95 whose opposite side-tootmsurf aces 96 and 9 7 are spherical. l ,-andd9l denote, respectively, normals to' the tooth surfacesyiifian'd 9'! of the crown gear; ;respectively, "-at the points .952 and I03, and 98 and 9a denoteyre'spectively, the

centers .of these sphericalsurfaces}. Tha -tooth surfaces of each gear; 90: and 9 i canbe? generated all directions through said conjugate to theicrownrgear fibyrotating a facemill .gear, cutter havingioutsidezand inside spherical cuttingiedgescentered;at': 98;1and- 99, respectively, ini engagement with a :gear blank while .producingiarelativeirolling motion between cut- .ter and blank. at a.ivaryingz-ratio-:-as though the blank were-rolling:Nviththecrown:gear 95 represented by the cutter. This will be .described fur- .therlater. I

. Fig.6: shows. thewpainof gears and!) l in mesh in aschangeover;position, that-:.is,-;in a position where the torque ratio b'etween the. gears is at oneextreme. Imthis position, the instantaneous .axis of rjotationzof the gearsis-at I05. The other extreme position of. the" instantaneous axis is denoted byJ 94.. Itwill. be noted that. in theposition .shown in; Lli'ig;v .6, the tooth- I06 of thegear 90 is .not'tsymmetricaliwithqreference to the center line 94.1. The departure fromxz'symmetrygin the design of the-.teethis. made in order to insure goodmeshiing action onithetwo sides c'o'fthe teeth when they aregenerattedz-withrd spherical-cutter. The dezparture from. symmetryjamay be made,v therefore, to balance the minimum radii ofcurvature on-the twosidesof the teeth.

- Rig..fiishows.thezposition:of the. gears where a tooth llliilsof. thej-geari9ll is-nearly on'center, with the. instantaneous .axisin its top position I 65. Fig .7 shows anotheriposition of the :gears where they; have rotatedsthrotigh::half a. pitch and a tooth I91 of the Y pinion iis nearly: on center with 'theinstantaneous axis in 'itss'lowest position I 04. Theopoints of contact between lthe' gear and pinionsteeth areznowv at rIB8Jand-JD9, and H0 and Ill :are nowi tooth; normals rat theipoints. of t contact. These again intersect thelinei ofazcenters v9t in'the instantaneous. axis gWhi'ChiiS now, asstated. at 194. '...The crown gear and the gears '99 and 9l-have undulating .pitch surfaces :as .determined by the shift of. positions of. the; instantaneous axes. It will.benoted;ihowever that in the case of the unsymmetrical;teethashowniin Figs. 6 and 7; the undulations of the-pitchw-surfacesjmay be unsymmetrical to the. center.- lines; 'of the gears in correispondenceto the-lack of symmetry-ofthe teeth.

Figs; 8 and; a9aillustrate5 diagrammatically one method of generating gearsjaccordingto-the pres- ,ent invention. particularlywith reference to the use of asphericalrfaceemillcutter asthe generating tool, Preierablyaboth sides .of: a tooth space of a gear-are,cutwsimultaneously. --In-Fig. 8 a spherical iaceemill cutter -l i5; is shown positioned to cutthe tooth surfaces-10f 'afpinion l-l6 whose opposite side. tooth-g-surfacesare --denoted at lZ'l and .128 in Fig. The cutter :I I5 has outside cutting profiles 1- 1 11 and :inside cutting profiles I it whose-centers are-at. H 9 andv l 2!], respectively, on the; axis 1 2 l IOfS the cutter. The axisof'the pinion is :denoted. at I 22"and;the axis of the mate gear is denoted at,.l2.9.; The common apexiof gear-and pinion is denoted:at-l23. .uIn' :cutting the, .geanwthei axis 1'25 of. the generating crown .gear i's 'preferably positioned perpendicular to the jrootjplane I 30. of the gear.

:In generating-the.zpinion ll6,-the same basic generating gearsmay bezusedras'forgthe gear, that isgethe; axis of the :cradle-may again be at I25. The cutter is preferably ipositioned,fhowever, so that-its'projected' axis i=2 l 'isperpendicular to the root planelflfi of I thex'pinion. Each tooth surfaceiof the pinion-may beegenerated then, by rotating the cutter i I I5. oncits' axis; I21: while the Work H6 isirotat-ed on its axis liTat-auniform velocity and whilel'avrelative. translatoryi movement-is producedmetweenztheicutter and work.

'11 at avarying'yelocityaboutthe "axis I25 of the basic generating-"crown gear. When a tooth surface or a pairof tooth surfaces is completed, the

cutter is withdrawn from engagement with the blank and the blank is indexed. Then the cutter is fed back into engagement with the blank and the next tooth surface or pair of tooth surfaces generated etc.

The translatory movement may, of course, be imparted either to the work, or to the tool. In Fig. 9 the translatory movement is shown as imparted to'the tool. vI-Iere'il8', H8", 8' and H8 denote four successive positions of the inside concave cutting edgesof the tool as the work rotates on its axis. The corresponding positions of the cutter axis during this translatory movement of the cutter are denoted at I2 I i2i", l2l' and I21, respectively. The positions of the tooth surface of the pinion, which is being generated during this'portion of the generating movementare denoted at (28', I28", 128" and I28, respectively. It will be noted that during this uniform rotation of the work, the cutter is moved at a-varying velocity.

The pinion H6 shown in the drawing has unequal addendum and dedendum according to standard practice in the automotive field, the addendum 'of the pinion tooth being considerably greater than its dedendum. The whole tooth profile l28-will be'rolled. out when the axis of the cutter has moved to the position 12h. The distancesa, b, c, d,"between successive positions of the cutter axis for equal angles of rotation of the work vary.- The distances c and d may, however, be. substantially equal on account of the rapid cycle ofvariation.

A gear conjugate to the pinion H may be generated by providing a cutter having spherical cutting edges of the same radii as on the mating tooth sides of the pinion teeth and using a basic member the: same as for the pinion generation.

The axis I of this basic member as already stated is preferably positioned perpendicular to the root plane I of the'gear.

The sphere centers ofthecutter for cutting the gear should also be disposed in thesame relationship with respect to the axis I25 as they were'in the generation of the pinion,'and the generating roll should be so modified from'uniform roll as required-to produce the desired-profile shape.

Lengthwise mismatch of the mating tooth surfaces of the gear and pinion may be obtained by providing a smaller radius on the inside cutting surface of both gearand pinion cutter than is employed on'the outside cutting surface of the cutter which produces-"the mating tooth side. Profile mismatch of the mating-tooth surfaces may be obtained by positioning the cradle axis so that it includes-a smaller angle with a line I29 perpendicular to the root plane I28 of the pinion than the angle between the axis I25 and this normal I29; When the two sides of the pinion are .cut in separate operations, profile mismatch may also be obtained by modification of the generating roll. In a single-side cutting operation, the axis l 25 of the cradle is frequently made perpendicular to the root plane of the pinion and parallel to the cutter axis.

When the two sidesof both members of the pair are cut simultaneously, the root lines pro 'duced usually do not pass. exactly through the ardtooth. Wherelargepressure angles are em- '12 ployed, however, the increase in tooth depth at the large end is slight and of nopractical dis-jadvantage.

While the invention has been described in connectlon with different embodiments, it will be understood that it is capable of still further modiflcation and this application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such. departures from the present disclosure as come within known or customary practice in the gear art and as may be applied to the essential features hereinbefore set forth and as fall within the scope of the invention or the limits of the appended claims.

Having thus described my invention, what I claim is:

1. A pair of varying-leverage gears, each member of which has tooth profiles that have distinctly different portions of small and large curvature, respectively, the portion of each profile which is of smallest radius of curvature being located near thepitch line of the gear. Z

2. A pair of varying-leverage gears, each member of which hasltooth profiles that have distinctly difl'erent'portions of small and large curvature, respectively, the portion of each profile which is of smallest radius of curvature being located near the pitch'line of the gear and the portions above'and below said portion of small radius being less curved than said pitch line portion.

3. A pair of varying-leverage bevel gears which have longitudinallycurved teeth and tooth profiles that'have distinctly different portions of small and large curvature, respectively, the mating tooth surfaces of the two members of the pair having different radii of lengthwise tooth curvature.

4. A varying-leverage gear, each of whose tooth profiles adjacent the pitch line of the gear is more curved than an'in'volute profile of the same pressure angle, and above and below said more curved portion is 'less curved than the involute profile.

5. A varying-leverage gear that has an undu latory pitch surface, the pitch of whose undulations is equal to the pitch of the gear teeth, and that has side tooth surfaces conjugate to spherical surfaces. i 6. A varying-leverage bevel gear having side tooth surfaces which are conjugate to spherical tooth surfaces and whose profiles have distinctly different portions 'that are of small and large curvature, respectively. 7. A pair of varying-leverage bevel gears, which have longitudinally curved teeth, opposite side tooth surfaces of each member of the pair being conjugate to concave and convex spherical surfaces, respectively, that'have differentsphere radii. the tooth profiles of each member of the pair having distinctly different portions of small and large curvature, respectively.

8. A pair of varying-leverage bevel gears which have longitudinally curved teeth whose opposite side tooth surfaces are conjugate, respectively, to convexand concave spherical surfaces of different radii of curvature, each of the'profiles of the teeth of said gears having distinctly different portions of-small and large curvature, respectively, the portion of each profile which is of the smallest radius of curvature being located near the pitch line'of the gear. 9. A pair of varying-leverage gears whose -Profi es have distinctly; different portions 13 of small and large curvature, respectively, and whose teeth are unsymmetrical with reference to lines connecting the axes of the two gears.

10. A pair of varying-leverage gears whose tooth profiles have distinctly different portions of small and large curvature, respectively, and whose teeth are unsymmetrical with reference to lines connecting the axes of the two gears, the portions of the tooth profiles which are of smallest radius of curvature being located near the pitch lineof each gear.

11. A pair of varying-leverage gears whose teeth are longitudinally curved and whose mating tooth surfaces have different radii of lengthwise curvature, the profiles of the tooth surfaces being differently curved in different portions of the tooth heights.

12. A varying-leverage gear whose side tooth surfaces have profiles that are differently curved in different portions of the tooth heights and whose opposite side tooth surfaces are conjugate to a basic gear whose side tooth surfaces are of circular arcuate profile shape.

13. A mating gear and pinion having tooth profiles including curves of action and outer tooth profiles of such shape that the common normal to their mating curves of action at their point of contact will cross the line of centers of the gears at a different point for different positions of the gears, and the same points will be simultaneously crossed by the common normal to a simultaneously mating curve of action and outer tooth profile,

14. A mating gear and pinion having tooth profiles including curves of action and outer tooth profiles, of such shape that the common normal to an outer tooth profile and its mating curve of action will pass through the same point in the line of centers of the gear and pinion that the simultaneous common normal to the mating curves of action at their point of contact passes, and wherein said point shifts substantially along said line of centers with rotation of said gears.

15. A mating pair of variable leverage gears having tooth profiles including curves of action and outer tooth profiles, of such shape that for each relative position of meshing engagement of the gears a point on each side of the profile of one tooth will substantially engage a point on 14 each of the adjacent profiles of the mating teeth of the other gear, and wherein common normals to the profiles at each contact point will intersect at a point in the line of centers of the gears, said point shifting substantially along said line of centers with rotation of said gears.

16. A pair of varying leverage bevel gears which have longitudinally curved teeth whose tooth profiles are differently curved in different portions of the tooth heights, the mating tooth surfaces of the two gears having different radii of lengthwise tooth curvature.

1'7. A pair of varying leverage bevel gears which have longitudinally curved teeth whose side tooth surfaces are tangent at mean points in their lengths to lines drawn radial of the gear apexes, the profiles of the tooth surfaces being differently curved in different portions of the tooth heights.

18. A pair of varying leverage bevel gears which have longitudinally curved teeth whose side tooth surfaces are tangent at mean points in their lengths to lines drawn radial of the gear apexes, the profiles of the tooth surfaces having distinctly different portions of small and large curvature, respectively, the portion of each profile, which is of smallest radius of curvature, being located near the pitch line of the gear.

19. A pair of varying leverage bevel gears which have longitudinally curved teeth whose side tooth surfaces are tangent at mean points in their lengths to lines drawn radial of the gear apexes, opposite side-tooth surfaces of each member of the pair being conjugate to concave and convex spherical surfaces, respectively, that have different sphere radii, the tooth profiles of each member of the pair being differently curved in different portions of the tooth heights.

ERNEST WILDHABER.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,009,915 Davis July 30, 1935 2,114,793 Bauersfeld Apr. 19, 1938 

